Details

Time bar (total: 12.1s)

sample180.0ms

Algorithm
intervals
Results
68.0ms86×body1280valid
65.0ms32×body2560valid
21.0ms65×body640valid
5.0ms28×body320valid
4.0ms81×body80valid
3.0ms67×body80nan
2.0ms14×body160valid

simplify47.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 48.2b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.5b
(pow (+ 1.0 (/ i n)) n)
11.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite93.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative
Counts
4 → 321
Calls
4 calls:
30.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
21.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
377.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
265.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
221.0ms
(pow (+ 1.0 (/ i n)) n)
355.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
013193734
150013446

prune899.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.4b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
14.3b
(* (pow i 2) (log 1.0))
21.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-prod-down pow-exp clear-num log-pow fma-udef
Counts
4 → 186
Calls
4 calls:
1.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
13.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
6.0ms
(* (pow i 2) (log 1.0))
5.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series687.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
224.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
167.0ms
(* (pow i 2) (log 1.0))
199.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify116.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07343209
137502968
250012968

prune721.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 8.9b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
0.3b
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
13.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
14.3b
(* (pow i 2) (log 1.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×add-cbrt-cube
20×associate-*r*
19×times-frac
12×pow1 associate-*l*
10×prod-exp
8×cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*r/ div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num log-pow
Counts
4 → 122
Calls
4 calls:
6.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
6.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
3.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
6.0ms
(* (pow i 2) (log 1.0))

series675.0ms

Counts
4 → 12
Calls
4 calls:
163.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
219.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
146.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
146.0ms
(* (pow i 2) (log 1.0))

simplify76.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (59.0ms)

IterNodesCost
04881787
123721525
250021522

prune420.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 8.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt n)
0.6b
(cbrt n)
13.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
14.3b
(* (pow i 2) (log 1.0))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
25×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
11×add-exp-log
9×times-frac
8×associate-*l* add-cbrt-cube
6×cbrt-prod log-prod
5×pow1
4×expm1-log1p-u unpow-prod-down associate-*r* log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in prod-exp associate-/r* associate-/l*
2×pow1/3 unpow2 sqr-pow
1×cbrt-undiv pow-to-exp frac-2neg div-exp pow-exp clear-num log-pow *-commutative cbrt-unprod div-inv
Counts
4 → 91
Calls
4 calls:
1.0ms
(cbrt n)
1.0ms
(cbrt n)
3.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
6.0ms
(* (pow i 2) (log 1.0))

series658.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt n)
189.0ms
(cbrt n)
139.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
147.0ms
(* (pow i 2) (log 1.0))

simplify41.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
0275826
1949747
25001736

prune377.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 8.9b

regimes181.0ms

Accuracy

68.6% (5.6b remaining)

Error of 16.6b against oracle of 10.9b and baseline of 28.8b

bsearch303.0ms

Steps
ItersRangePoint
9
5.175139968754377e+19
9.790829469375981e+26
5.2622542467923034e+19
11
-3253.153967321615
-8.303200230518375e-17
-0.0723466983079064

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05435
15435

end0.0ms

sample5.2s

Algorithm
intervals
Results
2.1s2947×body1280valid
1.8s986×body2560valid
555.0ms1803×body640valid
148.0ms847×body320valid
115.0ms2461×body80valid
78.0ms2184×body80nan
46.0ms442×body160valid
18.0ms5×body5120valid